Let A be an 5 times 7 matrix with rank 3 . If the the nullity of A is n; the dimension of the row space of A is m; the dimension of the column space of A is k, then n+m+k= ?

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Step:1 ：Given a 5 times 7 matrix A with rank 3, we have m = k = 3.Step:2 ：Using the rank-nullity theorem, we get 3 + n = 7. Solving for n, we find n = 4. Thus, n + m + k = 4 + 3 + 3 = boxed{10}.

Answer

Step: 1 ：Given a 5 times 7 matrix A with rank 3, we have m = k = 3.Step: 2 ：Using the rank-nullity theorem, we get 3 + n = 7. Solving for n, we find n = 4. Thus, n + m + k = 4 + 3 + 3 = boxed{10}.

Let $A$ be an $5 \times 7$ matrix with rank 3 . If the the nullity of $A$ is $n$; the dimension of the row space of $A$ is $m$; the dimension of the column space of $A$ is $k$, then $n+m+k=$ ?

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